Complex Number Magnitude Calculator | Find Modulus of Complex Numbers
Easily calculate the magnitude (or modulus) of a complex number online. Enter the real and imaginary parts, and this tool will instantly find the magnitude. Learn about complex numbers and their magnitudes.
Enter Complex Number
A complex number is of the form a + bi, where a is the real part and b is the imaginary part.
Result
Magnitude (Modulus):
The magnitude of a complex number z = a + bi is calculated using the formula:
$$|z| = \sqrt{a^2 + b^2}$$
Visual Representation on Complex Plane
Understanding Complex Number Magnitude
In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1. The real part is a, and the imaginary part is b.
The magnitude (or modulus) of a complex number represents its distance from the origin (0, 0) in the complex plane. It's a real number that gives the "size" or "absolute value" of the complex number.
Formula: For a complex number z = a + bi, the magnitude |z| is calculated as:
$$|z| = \sqrt{a^2 + b^2}$$
Use Cases: Complex number magnitudes are crucial in various fields such as electrical engineering (AC circuit analysis), quantum mechanics, signal processing, and more. They help in understanding the strength or intensity of complex quantities.